The Geometry in Space Project
Sponsored by the Indiana Space Grants Consortium and
Ball State University
Mars in Perspective
Your Mission
So far, your expedition has traveled from Earth to Mars and examined prospective landing sites using photographic and thermal images. In this activity, you will select one or more of these potential landing sites for further study. Your goal is to create realistic 3-D still images and animated fly-bys of these sites. Back on Earth, these graphics will be used to determine which of the prospective landing sites offers the best terrain for a future Mars spaceport, scientific research center, and colony.
Perspective Views
Because every photographic image is taken from a particular point of view with a particular field of view, and because photography makes near objects look larger than distant objects of the same size, photographic evidence alone cannot provide all of the information necessary to fully and correctly represent 3-dimensional objects, including buildings and landscapes. By changing your position as an observer, you change what you can see. In other words, by changing your position as an observer, you change your perspective. In order to avoid false impressions, an approach is needed that frees viewers of the biases imposed by a limited set of perspective views. At the minimum, maps or models that do not distort the apparent positions or sizes of objects are necessary. Better yet are interactive models that enable the viewer to see the objects of interest from any perspective.
The concept of a change in perspective is illustrated in Figures 1 and 2. In Figure 1, the drag point and vanishing points may be moved. Moving these points creates different perspective views of the box. When simulating such changes, think of the box as fixed and yourself in motion, rather than yourself as fixed and the box in motion.
Figure 1 Perspective View of a Box
- Move
Vanishing Point 1. How does your
view of the box change? What do
these changes suggest about your change in position as an observer?
- Move
Vanishing Point 2. How does your
view of the box change? What do
these changes suggest about your change in position as an observer?
- Move
the Drag Point. How does your view
of the box change? What do these
changes suggest about your change in position as an observer?
- What
feature(s) of this model contribute to its realism? How does the model fail to imitate
reality?
Artists and architects first developed the geometric basis for perspective drawing during the Renaissance in Florence, Italy. Leone Battista Alberti wrote the first general treatise, Della Pictura, on the laws of perspective in 1435. It was printed in 1511. Alberti’s method for creating a perspective view of a tile floor is seen in Figure 2.
Figure 2 Alberti’s Method
- Describe
the effect on the drawing of moving the vanishing point. Point P. The vertical line to the right of P.
- How
does your position as an observer seem to vary as a consequence of these
movements?
- What
feature(s) of the model contribute to its realism? How does the model fail to imitate
reality?
Modern mathematics and computer technologies greatly simplify the creation of perspective views of all sorts. In the next section, you will use one of those technologies to create perspective views of landscapes on both Earth and Mars.
Digital Elevation Model Data
In this activity, you will use digital elevation model (DEM) data to investigate the topography of landscapes on Earth and Mars. Using NASA and USGS DEM data and the terrain modeling tool 3dem, you will visualize landscapes from different points of view. First, however, you should understand what DEM data is and how it is obtained.
Radar imaging works like a flash camera in that it provides its own light to illuminate an area on the ground and take a picture. The fundamental difference between radar and photographic imaging is in the wavelengths of light used: Radar uses radio waves to illuminate the ground rather than visible wavelengths. Instead of a camera lens and film, radar imaging systems use an antenna to receive and a computer to record data.
Radar (RAdio Detection and Ranging) (See Figure 3) measures the strength and round-trip time of the microwave signals that are emitted by a radar antenna and reflected off a distant surface or object. These echoes are converted to digital data and passed to a data recorder for later processing and display as an image. Given that the radar pulse travels at the speed of light, it is relatively straightforward to use the measured time for the roundtrip of a particular pulse to calculate the distance from or range to the ground. This information is used to create a digital elevation model (DEM) of the terrain scanned by the radar.
Figure 3 Radar Imaging System
Like photographic images, radar images are composed of arrays of pixels, or picture elements. In the case of DEM files, each pixel represents the elevation of the ground at a particular point. Consequently the DEM data file itself is not a picture at all. It is just an array of numbers. One way of viewing an array of numbers is to assign each pixel a color based on its elevation. For instance, Figure 4 shows elevation data for the giant volcano Olympus Mons on Mars. In the figure, different elevations are represented using different colors. The arrangement of the different colors suggests a roughly conical form with a depression at the summit. Far more interesting images based on the same data are shown in Figures 5 and 6, created using the terrain modeling tool 3dem. The image of Mauna Loa, shown in Figure 7, was also created using 3dem.
|
Figure 4 Elevation Data, Olympus Mons |
Figure 5 3-D View, Olympus Mons [Scene width = 147 miles]
Figure 6 3-D View, Olympus Mons Cauldera [Scene width = 147 miles] |
Figure 7 Mauna Loa, Hawaii
[Scene width = 50 miles]
- Which
volcano is wider, Mauna Loa or Olympus Mons?
- What
is the approximate height of Olympus Mons?
A Tale of Two Canyons
In this section you will use DEM data to model two famous canyons, one on Earth (See Figure 8) and the other on Mars (See Figure 9).
|
Figure 8 Grand Canyon, Arizona [Scene width = 18 miles] |
|
Figure 9 Valles Marineris, Mars [Scene width = 100 miles] |
· Start 3dem
· Select File then Load Terrain Model then Digital Model (See Figure 10).
Figure 10 Loading a DEM
· Select USGS Standard Dem (See Figure 11).
Figure 11 Selecting a USGS Standard DEM file format
· Select grand-canyon-e.dem. When the image has loaded (See Figure 12) use the vertical and horizontal scroll bars to move to the lower left hand corner of the image. When you left-click the mouse a notched-box should appear. Drag the box using the left-button of the mouse. Rotate the notch using the right button. The box may be resized by using the left button to drag a corner. Position and resize the notched-box as shown.
Figure 12 Selecting a Scene
· Click on Show Scale (in feet) in the Color Scale window. The scene width indicates the distance across the notch box.
- On
average, approximately how wide is this part of the Grand Canyon?
- Approximately
how long is the portion of the canyon included in this data file?
· Select Operation then 3-D View and select the options shown in Figure 13.
Figure 13 Setting Terrain Projection Parameters
· Click OK on the Scene Colors window. You should obtain the image seen in Figure 14.
Figure 14 Perspective View of the Selected Scene
· Repeat the process outlined in steps several times, each time from a different perspective, as defined by the notch box. When you understand the procedure, recreate your favorite view and save the image by selecting File then Save Scene Image then JPEG and giving it the name canyon_favorite. Be sure to save the file on the desktop so you can find it later.
· The next step is to create a “movie” of a flyby of some landscape features. Returning to the notch box used in the demonstration above, select Operation then View Flyby instead of Operation then 3-D View. Set the Max Length to 20 Frames as shown in Figure 15. For dramatic effects, lower the Flyby Altitude to just above the landscape elevation. Of course, if you fly too low, you might crash into the canyon wall, so decide on a reasonable altitude.
Figure 15 Setting Flyby Projection Parameters
· After completing the Flyby, you may save it for later viewing. Select Operation then Animate Flyby then Color Animation and save the animation as canyon1 on the desktop. Be sure to set Key Frame Every ___ Frames to 5. The animation will step through each frame. When the animation is complete, you may view it by leaving 3dem, locating canyon1 on the desktop, and double-clicking it. The animation should then start automatically.
· Mars also has a grand canyon, named Valles Marineris, seen in Figure 16 as the large scar near the equator.
Figure 16 Valles Marineris
· To begin your exploration of the landscapes of Mars, open the digital terrain model tg15s067. Be sure to select NASA Mars DTM in the DEM File Type window. When the file opens, position the notch box as seen in Figure 17 and create both still and animated views of the north wall of this portion of the canyon (See Figure 18). Select Show Scale in the Color Scale menu to estimate the dimensions of the canyon.
Figure 17 Valles Marineris
Figure 18 Canyon Wall
- On
average, approximately how wide is Valles Marineris at its widest point in
this file?
- Approximately
how long is the portion of the canyon included in this data file?
- How
does the Grand Canyon on Earth compare to Valles Marineris on Mars?
Modeling Olympus Mons
Repeat the same procedure in an investigation of Olympus Mons using the file tg15n127.
- Approximately
how wide is the volcano Olympus Mons?
- Approximately
how wide is its cauldera?
- What
is the elevation on the rim of the cauldera?
- What
is the elevation on the floor of the cauldera?
- How
does Olympus Mons compare to volcanos on Earth?
- How
would you compare the details seen in photographs of Olympus Mons with the
details available in DEM-based models?
Review of Proposed Sites
To meet your mission goals, you must now create realistic 3-D views of one or more prospective landing sites.
- Create
four still images for each site
-
North-looking
-
South-looking
-
East-looking
-
West looking
- Create
two animated fly-bys for each site
-
South-west to north-east
- South-east to north-west
- Taking
all factors into consideration, which site would you recommend and why?
Related topics
- What is a map and what mathematics are at issue?
- What is a map projection?
- Is there a single, best projection? Why or why not? (See Figure 19)
- When making a map, if you strive for accuracy when representing the shape of land forms, what distortions are you likely to introduce?
Figure 19 Map Projections
- How do traditional topographic maps represent changes in elevation? (See Figure 20)
- How must you use imagination to visualize the shape of the land?
- What feature(s) contribute to the realism of the drawing? How does the model fail to imitate reality?
Figure 20 Topographic Maps
· Architectural rendering is often done using computer-based tools. Explore the capabilities of Design Workshop Lite (See Figure 21).
Figure 21 Architectural Rendering
- Landscape rendering is also done using DEM-based technologies. Explore the capabilities of GenesisII (See Figure 22).
Figure 22 Landscape Rendering
- Scientific visualization uses a variety of data types to better understand dynamic processes in nature such as weather, climate, and climate change (See Figure 23).
Figure 23 Scientific
Visualization